This is a difficult subject to teach. First of all, what kind of University are you preparing them for? Are they going to go to attend an international program or a regular Thai program? If they are going to an international program or an overseas university they will need to work on the 4 skills: reading, writing, speaking and listening. I would recommend using either an IELTS or a TOEFL prep book that comes complete with a CD for the listening sections. If your local bookstore doesn't have a good book, you can torrent one with the book on PDF & some MP3s included. I actually prefer the ebook, as I can print out sections for the students and it's easier the play the MP3s than the CD!
If they are attending a regular Thai program, speaking, listening and writing will probably not be required, typical entrance exams will just be grammar & maybe vocab questions - though you should double check this rather than just taking my word for it!
I would use the material that you have been given as a diagnostic tool. Have them do the exercises as though they were taking a test (good practice for them!) and then see which type of questions gave them the most trouble. Once you've identified what they need to work on, I would recommend using either one of Raymond Murphy's or Betty Azar's grammar books as your source for lesson material. Murphy uses British spelling and grammar and Azar uses American, but she also points out the British spelling and usage so that students will be aware of the difference. Their books should be found in any good bookstore or can be torrented. Azar also has a website will lots of free material to supplement the books. Welcome to AzarGrammar.com